Solve the Multiple-Angle Equation $\sin \frac { x } { 2 } = \frac { \sqrt { 2 } } { 2 }$

Multiple Choice

Solve the multiple-angle equation.​ $\sin \frac { x } { 2 } = \frac { \sqrt { 2 } } { 2 }$

A) ​​ $x = \frac { 2 \pi } { 3 } + 2 n \pi \text { and } x = \frac { 5 \pi } { 3 } + 2 n \pi$ ,where n is an integer
B) ​ $x = \frac { 7 \pi } { 6 } + 2 n \pi \text { and } x = \frac { 11 \pi } { 6 } + 2 n \pi$ ,where n is an integer
C) ​ $x = \frac { \pi } { 2 } + n \pi$ ,where n is an integer
D) $x = \frac { \pi } { 2 } + 2 n \pi \text { and } x = \frac { 3 \pi } { 2 } + 2 n \pi$ ,where n is an integer
E) $x = \frac { \pi } { 2 } + 4 n \pi \text { and } x = \frac { 3 \pi } { 2 } + 4 n \pi$ ,where n is an integer